January 19, 2012

Shortage of female math geniuses not due to "stereotype threat"

Men are over-represented at the high end of math performance: there are more male math geniuses than female ones.

A theory that was proposed to explain that fact is that of stereotype threat. According to this theory, there is a stereotype in society that "women are bad in math"; women internalize this stereotype and lose confidence about their math abilities, and so they tend to perform sub-optimally in math tests, hence rendering the idea of "women are bad in math" a self-fulfilling prophecy.

This new study demonstrates that much of the literature that has accumulated around the idea of a "stereotype threat" can be relegated to the trash bin, and those who hope that fighting the stereotype will lead to more females joining the mathematical elite have their work cut out for them.

Can stereotype threat explain the gender gap in mathematics performance and achievement?

Stoet, Gijsbert; Geary David C.

Men and women score similarly in most areas of mathematics, but a gap favoring men is consistently found at the high end of performance. One explanation for this gap, stereotype threat, was first proposed by Spencer, Steele, and Quinn (1999) and has received much attention. We discuss merits and shortcomings of this study and review replication attempts. Only 55% of the articles with experimental designs that could have replicated the original results did so. But half of these were confounded by statistical adjustment of preexisting mathematics exam scores. Of the unconfounded experiments, only 30% replicated the original. A meta-analysis of these effects confirmed that only the group of studies with adjusted mathematics scores displayed the stereotype threat effect. We conclude that although stereotype threat may affect some women, the existing state of knowledge does not support the current level of enthusiasm for this as a mechanism underlying the gender gap in mathematics. We argue there are many reasons to close this gap, and that too much weight on the stereotype explanation may hamper research and implementation of effective interventions.

34 comments:

The difference is genetic. The advantages of X over Y are as marked as the advantages of Y over X. Are there exceptions to the rule? Always. Is there a norm for X? Yes. Is there a norm for Y? Yes. Intelligence has nothing whatsoever to do with the demons that drive us, and these are as different as X is to Y, and night is to day. That which distinguishes us makes us different on various levels by giving one an advantage over the other, and the other an advantage over the one. Who knew hunters could usually hunt better than non-hunters? Is it social conditioning or something else? This is genetics not psychology.

I was just reading about this yesterday. Men asking why there are no female geniuses. Of course, that depends on what your idea of genius is, for me it means the person left a group of works with lasting quality, not a high IQ. But don't men forget that most women choose to take time off to have children and raise them? You can't be a genius if you're surrounded by all these diapers needing to be changed and runny noses. I read somewhere, don't recall where, that even men can't be geniuses if their family life is too much of a bother for them.

Charles,Since the 1960's at least the answer would most likely be yes, for the Western World.

Alice,The only way to compare "Genius" in Match or elsewhere is to have an objective measure of it, one such is High IQ or in the case of Math, winning the Fields Medal. Objectively at the right tail of the bell curve, men outnumber women in Math ability over 10 to 1. Subjectivity doesn't count here.

I also have a daughter who was recognized (tested) and found to be a math genius in 7th grade. It first expressed itself in music in 6th grade. She suddenly started playing sophisticated classical type scores and yet had never had a single lesson. When I asked her about it, she said, "Its all math, Mom." I couldn't find a school that could help her develop. Eventually she received a full 4- year scholarship to Westover in Middlebury, CT. This exclusive girls boarding school specializes in developing girl math genuises. From there, my daughter went (again on a scholarship) to Oberlin in OH where she studied quantum physics.

And like clockwork we get comments about the supposed advantage boys have, to explain why their are more men at the top, without also mentioning that there are also more boys in special education classes than girls.

@Charles

Boys are doing worse at all levels if education and their are more boys in special education than girls. We should not try to tear successful males down at any opportunity and then selectively ignore all the males at the bottom. It doesn't make sense that boys are incouraged more in an environment that us mostly set up against them. Whether you want to use sociology or individual biology to explain males greater success you can't ignore men's greater failures.

When I was a little girl I was a math genius in school. Next grades I hade lousy results and then I decided, when adult to study during evening, I got the highest degrees in math, but it is not me, it is my husband that is a Professor at a university.

And why, because I'm totally at his service at home. Clean sheets in bed, clean clothes, socks... I even buy books and choose interests for him, I arrange our/his travels... food...gardenwork, Im even a carpenter, plumber etc sometimes.

I do not think the difference is genetic, here. It is a need of society. More men are required to work and reserch, and just as many women who take care of these men. With the "disadvantage" to care for children and families, as usually happens. From the biological point of view, most girls who are convinced they are not gifted in mathematics spread, and most would be those that show themselves able in this matter. But evidently it is not so.It is true, we carry a big stereotype about when women could not prevail in these fields, but today is not so

But women still feel pressured to have children, and if you've never had any, you don't know how much time and effort it takes in raising them, much more than other "hardship." Most people can deal with hardship, it doesn't take a genius (no pun intended) to deal with hardships now and then, but I know that raising kids well is an extremely difficult and time-consuming job, and it WEARS YOU OUT.

And btw, this thing about hardships really isn't true. In a study done, it was found most geniuses came from comfortable middle class families. It seems if you're either too poor or too rich, genius eludes you as well.

Just for clarity, when I said "the supposed advantage boys have" I was talking about the myth that boys are given more support in education.

The idea is ridiculous given that boys are doing worse overall and that this gap had been growing for the past 20 years while little was done to address the "boy crisis. (There gas actually been more aid going to girls) Obviously boys should be doing as well and we know that girls do not have higher iqs.

But this not be the case. Based on iq or actual achievements boys should be seen as gifted as girls if not more. In fact there should be more boys in schools for the gifted seeing how boys are over represented on BOTH the low end and high end of the iq spectrum. But we only see mire boys in special ed...

The people saying we give more encouragement to (gifted) boys are using old talking points and ignoring the realities boys face. It will probably take ten years before people can actually look at what's going on.

It seems that feminists and other egalitarians tend to see the average differences in male and female abilities as a *problem* to be somehow "solved" with social policies. It seems obvious that Nature has an extremely strong tendency to bifurcate (split into two) gender across nearly all species. We are mammals and all mammalian species have two genders with non-identical roles and abilities. Of course men and women have many similar abilities and can adapt somewhat to different roles but our biological socio-gender orientations are not identical and they are not supposed to be either.

Feminism as an ideological and political tendency seems to have its historical location in what we may call the proletarianisation of the population, where late industrial capitalism has made us essentially "workers" who sell our labour. Globalism has the same tendency to negate ethnic differences and reduce us to worker-citizens. But humanity obviously isnt all about obliterating the differences between sexes and ethnicities even if that is what capitalist liberaism wants. *Difference* is an extremely important facet of "human being". Indeed *difference* is transcendental to all higher life and I think that we would have to go back to some very basic single cell lifeforms to get identity or equality.

The egalitarians seem to have not merely a social agenda but also a eugenics agenda: they wish to use social policies and agitation to direct human evolution down a path where differences are obliterated in the name of some "moral" crusade of "equality", "tolerance" and whatever other buzz words. But their project seems radically contrary to the basic principles of mammalian life, if not of *all* life. Sure it seems "good" if women obtain higher abilities but is the basic egalitarian orientation mistaken? Im not against social policies that direct human genetic development but it seems that eugenics should work *with* Nature rather than against it. Quite what that means is obviously open to debate but I think that it is worth noting that most feminists and other leftists are overtly dead set against any form of eugenics but in fact their own policies are radically eu/dis genic.

In my opinion egalitarianism will have a very high price (social collapse) because the well-being of society depends on its good order. You have to have good leaders to make good decisions, for instance, and supposedly "moral" democracy is no substitute for meritocracy, as Plato explained long ago. We have inherited a highly advanced technological society from the past and we are able to prosper because of the abilites and common sense of past generations, at least for a time but their world is rapidly changing into something new that will have to take responsibility for itself where social stability and progress is concerned. My fear is that democratic egalitarianism (and feminism, multiculturalism etc.) is actually a forefunner to *tyranny* as Plato noted, even to the "worker state". Mensheviks believe that capitalist society will gradually prepare the way for World Communism and cultural Marxism is aimed at preparing or hastening the transition.

As for the idea that differences of ability are due to "discrimination" (another favourite leftist buzz word), we have had harsh "reverse discrimination" in the UK for decades. You could lose your job for saying that men and women have different average IQs let alone races, especially in the public sector. All are obliged to promote "equality" 24/7 or be ostracised and/ or have their career and their lives ruined. A lot of people seem to think that is a great idea and a sign of "progress". Afterall, equality is "good" and society used to be "evil".. right?

Don't even try to feed me the sentiment that raising kids is the "hardest job in the world". The hardest jobs are things like crab fisherman, working down in mines that might collapse, being deployed in battle, etc... Stay at home moms have it pretty easy and if you can't see that you aren't cut for the difficult high stress jobs at the top (one readon I think men have a shorter lifespan). Those mothers aren't even having to collect water from a well, wash clothes at the river, gather wood, build fires, pluck chickens, make pottery and textiles to sell, and so on. Homes used to be places of production and work but they are far from that now. They stay at home dads I talked to also confirmed this.

And sure, most well achieved scientists came from well off backgrounds but not all which is the point. Essentially every major scientific breakthrough has come from men even though not all those men were given much opportunities... Instead they made it happen. The hardships I was talking about were people like Euler who became nearly blind but continued to write prolifically by doing many of the complex calculations in his head and relying on a near picture perfect memory. Im also talking about Stephen hawking who can only get his ideas out through painstakingly tedious trial and error as he compress with his physical disability. That and he also has to do many complex calculations in his head.

Then there was Einstein who came up with the theory of relativity, not in a university, but while working in a patent office.

So please, enough with the excuses and self congratulations. You won't get anywhere with that attitude or ever be like the people you casually dismiss as having "petty" hardships.

It is truly difficult for someone from Mars to empathize with a person from Venus, and visa versa. Best to keep it genetic, and even then, limited to the essential 1.5% of human genes that make us different from chimps (and all the other lifeforms in this section of the Universe).

What an ill informed discussion. There are no female math geniuses? Rubbish.

What about Hypatia and Ada Lovelace. There were MANY others. Not bad given the fact that educating women has been very strongly discouraged for millenia. Wisewomen were even burnt as witches.

http://www.agnesscott.edu/lriddle/women/chronol.htm

Women do better at all levels of objective education mostly because they are more likely to behave. But even in my generation the brightest girl at school was not allowed to go to Uni by her family. I myself caught myself instinctively down-playing my intelligence for social acceptance when I moved from single sex to mixed education. Women fall behind as soon as they are judged subjectively rather than objectively.

When I had my first child all of a sudden I was no longer invited to join committees in the same way as previously. It was instantaneous, like a switch had been thrown. Suddenly I was in the female basket rather than the true colleague basket. Unclean, Unclean.

Modern "geniuses" are about self promotion and patronage. Steven Hawkings is the classic. We dont yet live in an equal world.

There may be real differences between men and women but they do not delineate genius and non genius. Its way more complicated than that.

I myself caught myself instinctively down-playing my intelligence for social acceptance when I moved from single sex to mixed education.

Wow, that is so meaningful seeing how you can speak for all women and go inside the minds of men...

I just showed you that people are more likely to see girls as being gifted. That means girls are getting the recognition and the educational support. Your talking points are old and destructive when you act like there is all this favoritism towards boys even though its mostly the other way around.

Women do better at all levels of objective education mostly because they are more likely to behave.

I've heard this before; as soon as boys start doing worse its their own fault... Yet somehow you can make excuses for yourself and other grown women.

This is where learning style enters in. Schools have become a place that is mostly focused on good behavior (which they define as girl behavior), and of course following directions, due diligence, and repeating what your told. Then you can get your A. They don't value high energy or independent thinking. In my experience high school was more about diligence than intelligence. That's why I didn't do well until I got to college.

It's almost amusing that you would call girls more "well behaved" knowing that they fit into the classrooms better, then wonder why there aren't more female geniuses creating revolutionary ways of thinking by breaking with convention.

The reason I called the stereotype that boys are misbehaved as lazy is because it reflects a lazy way of educating. The low energy and obedience desired in most classrooms is not conducive to great thinking but mediocrity. We should be valuing the energy of boys and their creative ways even if it costs us more energy to do so. I personally think we need to have more male teachers since they will be more understanding of boys. On a very related issue, male teachers bring more confidence and drive to boys and girls.

I don't know if women haven't done much genius work because of biology or culture but I know they won't do it with the typical attitudes I've seen perpetuated here. To be capable of greatness you can't say things like motherhood is so HARD, and even diminish hardships other scientists went through like war, near blindness, disabilities, and producing works from prison! Not only does calling motherhood HARD sound spoiled but it also looks like they want recognition more than actual achievement. (Also, fathers rights maybe?!?) On a similar note women also need to stop spouting higher grades in grade school or greater diplomas received as "objective" evidence that great things should come of that. It's just celebrating more mediocrity given that neither requires much intelligence. On behalf of history they need to admit, at best, a lack of boldness and risk since some of the greatest scientists where never given an education or a title; men weren't always given things, sometimes had to take it upon themselves.

Mostly women just need to stop whining in search of recognition as if they want others to fix their problems (that actually fits perfectly with their traditional gender role) even when it just comes down their own choices, not the law.

This woman writes on actual female empowerment(owning your shit, not the "I'm forever a victim" that feminism is.

I don't understand people.With all my respect, why are people so coward to shout the truth against all this stupid propaganda?Do we really need a *** study to know that the proportion of men who excel in advanced maths ARE WAY MORE than that of women???Seriously? Call me whatever you want, but you can't change what I myself have witnessed in my entire life in two different cultures Egypt and the UK, and I myself am a top achiever in mathematics (usually top in my university and previously school).

We are not talking about "genius" here, we are talking about achievements in MATHEMATICS specifically.

Women are simply bad at high level mathematics compared to men, whether you admit it or not.

Why shouting the truth makes me labelled as ignorant or whatever now?

This article is like saying:"After extensive research we have found that men are better soldiers." OH REALLY !?? GOD KILL ME !!

@apostateimpressionsCan I please get your email or some other way of communication? I'm really interested in talking with you, as you seem to know a lot about exactly what I'm interested in.This is my google+:https://plus.google.com/118324267150724175776/posts

When you bring in the Fields medal, remember you are talking about the 99.999999th percentile or so. That far down the tail, there are so many influences that one would clearly expect individuals advantaged in a large number of ways to have a decisive ... well, advantage.

At the 99th percentile level, there are no differences in math ability in many cultures. How about at the 99.9 to 99.999 percentile? In Germany, as an example, about half of Mathematics students at the university level are women. And, while 30 years ago fewer than 10% earned a doctorate, today it is close to 30%. What best explains this incredibly quick advancement in the "math-intellectual ability" of German women? Societal changes, such as acceptance, of course.

@Prince"Wow, that is so meaningful seeing how you can speak for all women and go inside the minds of men..."

Huh? When did I do that?

@AhmedEgypt certainly does not offer equal opportunities for men and women.http://www.ungei.org/news/egypt_1747.html

Both my grandmothers (UK) were forced out of education in primary school. My mother's mathematics teacher expelled ALL the girls from class for the rest of their studies in high school over some petty thing, just an excuse really the teacher apparently felt teaching girls high school mathematics was a waste of time.

Years later I discovered that when I studied for my 11+ exams (not in the UK) there was a substantially lower pass rate for a boy as compared to a girl. So a girl could get a higher grade and not get into one of the high schools, therefore she had to go to one of the very rough technical training colleges (focusing on typing and other manual skills). The reason for this was apparently there were more high school places for boys than girls, and it was felt that the boys would catch up. At that time it was no longer true as shown by examination results.

Boys used to sail past in primary school, then it was high school, then Uni, now it is in the workplace. This is not a biological change, its societal, as Eurologist said.

When I said behave what I mean is that in school (especially Kindergarden) some boys are bouncing in their seats whereas the girls mostly sit and obey. It seems to be biological, not their fault. A need for more physical activity. This is why it is often said that boys should start school later as they are not ready. I have a well-behaved older son and a very bratty daughter, but it still applies. She can concentrate and he gets distracted and needs to move around. But he still tells her every day how much cleverer he is. She sincerely believes him. :)

It is true that some of these bouncy boys get discouraged and left behind. This needs to be fixed, but it is not the girls fault, it is the way education is delivered, AND HAS ALWAYS BEEN DELIVERD (ie sit still and do what you are told to do). But in the past a boy could feel some pride that at least he was doing better than the girls. Do we really need to smash down the girls for the sake of the struggling boys? In what universe is that an ethical solution?

I came across this quote which I think gets to the nub of the problem and also part of the solution."Specifically, girls at all levels of academic ability did better in single-sex schools than in coed schools; whereas for boys, the beneficial effect of single-sex schools was significant only for boys at the lower end of the ability scale. For higher-achieving boys, there was no statistically significant effect of school type on performance, positive or negative. "http://www.singlesexschools.org/evidence.html

@RoyI'd settle for equivalent.

Bigger is not always better. :)

Neanderthals had bigger brains. In all Dienekes skull studies I cant recall a correlation between craniums and IQs and I would not expect one,(excluding the clinically impaired of course).

@Annie MouseI can't post a complete reply now, but just a note:the link you providedhttp://www.ungei.org/news/egypt_1747.html

doesn't apply to me and what I said at all.That's a rural area, yes they have difficulties in education and traditional ideas.I come from the capital from a very populated area, where you can find schools everywhere, and girls don't go "help their fathers on the land"My parents are both of the working class, not farmers, and my sister is a doctor.

Boys are more likely to be dealt with as learning disabled and less likely to be realty with as gifted than girls. There is definitely a bias in who's giftedness we are supporting, and it consists of girls over boys!

Teachers may be fuelling the gender gap in education by stereotyping boys as badly behaved, research suggests... It emerged that pupils from all ages were more likely to identify girls as being better behaved and harder working. Even boys were more likely to pick out girls as high achievers, researchers said.

Children were also split into two groups, with the first group told that boys did not perform as well as girls. Both groups completed maths, reading and writing tests. The study found that girls’ results were broadly similar in both groups but boys in the first performed worse than those in the second.

This is a serious problem if boys are already considering girls as better achievers and it is likely affecting their success. One really has to wonder what environment boys are being taught in. I don't think it helps that most teachers are female and probably don't deal with the style of boys as well.

They make more effort to please them, display greater self-esteem and are more likely to believe they are being treated fairly.

The findings are particularly significant as more than a quarter of primary schools do not have a single male teacher...

Researchers found that women teachers may also unwittingly perpetuate low expectations of boys and encourage girls to work harder by telling them they are clever.

Unless you guys think that more girls deserve to be in schools for the gifted then please wake up. Some of you are defending the higher end of male achievement, which is fine, but boys are suffering across the board. It's not due to biology or lifestyle choices as has formed most of this debate. They're young boys who aren't even being given a shot because we are failing to develop them by... neglect, misunderstanding, resentment, or what have you.

I'm saying that the debate is at the wrong end of the picture. And if you believe that the genius gap comes from culture then to ignore boys development is to seek revenge on them. If you believe the gap is due to biology then you know boys will continue to be ignored while the focus remains on only the top males as the majority and lower end males get completely screwed.

The talking point of inequity towards females is old or misrepresented at best; don't perpetuate it or be baited by it. Start asking why boys are doing worse by every measure... Nobody should be agreeing with that.

That's the point! When women are doing worse you call it culture but when boys are doing worse you call it biology...

>This is why it is often said that boys should start school later as they are not ready

Gee, I wonder why boys aren't doing well with prevailing attitudes like this...

Ever consider that when boys are acting up and playing games they're actually engaging their minds a hell of a lot more than what they'd get from just learning the times tables or doing an art project? When they play they're planning, socializing/negotiating, harnessing their drives, and basically being INVENTIVE.

It's not "bouncing around" or being easily "distracted" unless you demand they act like girls and nothing else.

"Do we really need to smash down the girls for the sake of the struggling boys?"

Actually I've shown that male teachers would significantly help the situation (one other thing men are good at besides "boasting"). Maybe more male teachers would mean boy behavior isn't frowned upon. It should actually help girls too.

Lol. Clash of the genders here. "Everything must be equal in the possibilities" is the religion for some here. But as the genes tell us, there are differences, also between the genders. Even if cultural behaviour plays sometime an important rule, the basical differences remain.

"That's the point! When women are doing worse you call it culture but when boys are doing worse you call it biology..."

No. What I am saying is that there are plenty of brilliant female mathematicians despite the stereotypes.

What I am saying is that girls failed to achieve educational milestones in the past NOT because of biology but because they were actively prevented from doing so. And this is ongoing, although getting progressively better.

I am saying that when I visit kindergarten that almost all the girls are sitting quietly and a noticeable portion of the boys are wriggling around around, flicking stuff at the other kids, staring at the ceiling etc. I assume it is biological but I suppose it could be already be differential parental expectations/training. Anyhow the result is the same. They dont learn as much as a result, and distract the others. They fall behind and its worse in mixed classes where they compare themselves to the girls and there is more posturing (on both sides).

There is no malevolent society of evil female teachers plotting to discriminate against the boys. I dont beleive the boys are treated differently. Some boys however perhaps find it easier to respond to male authority as opposed to female authority. Apparently even something as simple as voice pitch makes a difference. Perhaps it is precisely the boys who have trouble obeying female teachers who are worst hit when they realize the girls are doing better academically. A vicious circle leading to discouragement and a negative self view.

Anyhow I agree that the problem of under-performing boys needs to be fixed.

Anyhow I agree that the problem of under-performing boys needs to be fixed.

Annie, As a father of one, I agree.

My son had a kindergarten teacher who expected 4-year-olds to sit still and try writing letters for hours on end. Wrong expectation - although girls complied and were the only ones getting rewards at day's end.

In California, the epiphany was that statistics showed: pupils who read a lot early do well in school. Ergo, all we need to do is teach 4-6 year-olds to read plenty and early, and everyone will be smart and live happily ever after. As a consequence, any other topic area, anything creative, and any kind of teaching that actually followed natural child development was nixed.

And yes, most teachers are female up to and including middle school, and there is a strong misunderstanding and bias against "unruly" boys. This is also a very well-known problem in public schools in the US at large.

However, come late high-school and college/university, the tables are turned.

I am a female college senior who found this article after googling for an answer to my higher math frustrations. To be clear, I am not a mathematics major, though I will have nearly completed all of the courses to finish a math degree by the time I graduate and plan to get a PhD in a quantitative field. I am currently the only woman in one of my college's upper level math course and I am also currently the only person in the class with a C average. I can also say with certainty that I spend the most time on my homework and get the best grades on assignments, but I fail to do well on the exams.

Perhaps part of this is test anxiety. Sure, I could always study more. But at a certain point in every math course I've taken (happened yesterday), I have to have a cry over the fact that the boys always do so much better than me (and most of my female friends when they are in my classes) with less effort.

Quite honestly, there are times when I think that it is unfair that I be graded against the same standard, but I know would be, in fact, very unfair to my classmates! I do feel deep down though that once I am actually doing my own research that it won't matter who got a better grade in some class. I believe that my capacity for creativity and innovation will launch me above most of the men in my field. One of my female math professors has basically expressed the same hope to me about her own research.

In short, I agree with many of the posters here that there are many more male math geniuses than female math geniuses. At the same time, I really believe in the value of women entering quantitative fields. In today's world, computers can handle many complex computations. What we need now are for women to struggle through the math to go on to be real innovators.

Now, this might not be completely satisfactory to people who say, well, we shouldn't pay attention to women's mathematics education/achievement because they won't receive the Fields Medal. What I'm saying, though, is that maybe we need to rethink the goals of an education in mathematics. Women have so much to offer to STEM, even if not all of us get perfect grades.

Stereotype Threat is THE fundamental reason why there are so few female math geniuses. I look at my own life as a woman and see the havoc that negative stereotypes about my gender has wrecked on my life and the lives of my female friends. For example, in college I studied anthropology because I believed that you need to have "innate" abilities in math to do well in math-related subjects. I struggled in math, engineering, and physical science courses and promptly decided that I was too stupid to do major in mathematics. After college I found myself hired for job as a web developer. Years after that I decided that software engineering was interesting and enrolled in a C++ course at local university. After finishing the course easily with an A grade I considered the possibility that I might be good at programming and decided to take some undergraduate computer science courses. Well, one thing led to another and I ended up being accepted to a master's in computer science program at a top 20 university. I am struggling with programming right now, but have found discrete math and all the math used in my computer science courses to be easy. So, I have finally realized that I've come full-circle and that 10 years later I am back to where I was in college--passionately curious about mathematics and fascinated with the relationships of numbers and numerical puzzles. How did I get here? By peeling off the layers of lies that our society has taught me as a woman about my abilities in math. I have discovered that I AM REALLY GOOD AT MATH. Now at the age of 38 I am exploring exactly how good at math I really am. At the time of this post I am getting ready to take my first graduate math course a top 10 mathematics department in the U.S. In the past month I have taught myself college-level linear algebra from the school textbook to prepare for the graduate course in spring. I thank my own insight into the lies our society has fed me and inspiration by other women geniuses in STEM fields, as well as unusual women with incredible numerical skills like Shakuntala Devi to assure me that a woman like myself can quite possibly be a math genius. I guess only time and a PhD will tell...

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